MISSION DIRECTOR'S SUMMARY

As of Mission Day 451, the Gravity Probe B vehicle and payload are in good
health. All four gyros are digitally suspended in science mode. The spacecraft
is flying drag-free around Gyro #1.

As reported last week, gyro #3 transitioned into analog backup suspension
mode during the first phase of a calibration test that began on Thursday,
7 July 2005, that involves electrically "nudging" the gyro rotor
to various pre-defined positions within its housing. We restored gyro #3
to digital suspension last Thursday evening and continued phase 2 of the
test last Friday. We suspected that the root cause of the transition to analog
mode was likely due to a known “race” condition, which occurs
when the gyro rotor reaches a low threshold, set by the hardware. For this
reason, we suspected that gyro #3 would transition to analog mode again during
the second phase of the calibration test, and this was the case last Friday.
We again returned gyro #3 to digital suspension and completed the test successfully.

The Poker Flats ground station in Alaska has been experiencing hardware
problems, and for this reason, we have had to re-schedule some of our data
telemetry sessions at other NASA TDRSS ground station facilities. We have
recently run tests at the McMurdo station in Antarctica, and we successfully
completed a data capture session from McMurdo this past Monday, 11 July 2005,
after some last-minute scrambling to get the connection properly set up.
We have also been using the Wallops ground station in Virginia.

On Wednesday, 12 July 2005, we completed a paper simulation of the calibration
procedures we will be performing towards the very end of the mission, just
before the helium runs out, to move our telescope from our guide star, IM
Pegasi, to a nearby star and back to IM Pegasi.

Yesterday, 13 July 2005, marks the one-year anniversary of our full-speed
gyro spin-up in space (gyro #4 was spun up to 105 Hz/6,300 rpm). That was
a very tense and exciting time in the Mission Operations Center (MOC) here
at GP-B. Also yesterday, we used ultraviolet light to reduce the electrostatic
charge on all four gyros. Very small amounts of charge build continually
build up on the gyro rotors throughout the mission. When the charge build-up
reaches a sufficiently high level, we use ultraviolet light to reduce the
charge. We last performed this procedure on during the week of 15 April 2005,
and you can read a more detailed description of the process in the Weekly
Highlights archive, here on our Web site: The results of the discharge
are included in the Mission Status table, shown above.

MISSION NEWS—STELLAR ABERRATION: NATURE'S GIFT TO GP-B

In our Mission News story of 6 May 2005, we described the telescope dither
and its important role in correlating the gyro spin axis orientation with
the telescope orientation during the Guide Star Valid period of each orbit.
In this week's Mission News, we describe the phenomena called “aberration
of starlight” (or “stellar aberration”). As GP-B Principal
Investigator, Francis Everitt, once put it: “Nature is very kind and
injects a calibrating signal [the aberration of starlight] into GP-B for
us.” This phenomenon actually provides two natural calibration signals
in the relativity data that are absolutely essential for determining the
precise spin axis orientation of the gyros over the life of the experiment.
However, the word “aberration” typically refers to behavior that
departs or deviates from what is normal, customary, or expected--and usually,
such behavior is not welcome. So, what does aberration have to do with starlight?
And, why would we want to use something aberrant as a calibration signal?
To answer the first of these questions, we must first travel back in time
to the 18th century.

At the beginning of the 18th century, astronomers were still seeking some
form of direct proof of the Copernican theory that all the planets in our
solar system orbit around the Sun. One such person was British Astronomer
James Bradley, who in 1718 was recommended by the Astronomer Royal Edmund
Halley to become a Fellow of the Royal Society, and who eventually succeeded
Halley as British Astronomer Royal in 1742.

Starting on 3 December 1725, Bradley observed the star, Gamma Draconis,
through his telescope and noted its position in the heavens. He was planning
to observe the star's position periodically for a year, anticipating that
in six months, he would be able to view a shift in the star's position due
to stellar parallax caused by the Earth having moved around the Sun to the
opposite extreme of its orbit. Parallax is the effect whereby the position
or direction of an object appears to move when viewed from different positions.
You can easily experience parallax by closing your right eye and viewing
a finger at arm's length with your left eye. When you switch viewing eyes,
closing your left eye and opening your right eye, your finger appears to
have moved to the left.

In Bradley's time, the prevailing wisdom was that the distance across the
long axis of the Earth's orbit--approximately 300,000,000 km (186,000,000
miles)--would provide a sufficient baseline to view a parallax shift in the
star's position. What the astronomers of Bradley's day did not know is that
even the closest star to our solar system is nearly 150,000 times further
away than the distance across Earth's orbit, and thus the parallax effect
between December and June observations of Gamma Draconis only amounts to
about 1.5 arcseconds (0.00042 degrees). This is an angle about the size a
pea, viewed from one kilometer away--much too small to be measured with instruments
of Bradley's day. It would be another 100 years before stellar parallax was
actually detected by Friedrich Bessel, director of the Konigsberg Observatory
in Germany.

Out of curiosity, Bradley made a second observation of Gamma Draconis two
weeks after his first one, and he was astonished to find that the star had
already shifted position--but by a greater amount than he expected, and in
the “wrong” direction for parallax. Bradley continued making
observations of this star's position over the course of the following year.
To his further surprise, he discovered that the pattern traced out by the
star's motion was an ellipse. Moreover, the major axis of the ellipse coincided
not with the long axis across Earth's orbit from December to June as would
be expected for a parallax measurement, but rather with the short axis from
March to September.

Bradley pondered these seemingly mysterious results for two more years,
discovering that all other stars he observed also traced out identical elliptical
patterns over the course of a year. One morning in 1728, he had an “aha” moment
while sailing on a boat, watching the motion of a wind vane flying from a
mast. He noticed that the vane kept changing directions as the boat turned
to and fro, and that it did not necessarily point directly opposite the boat's
direction of travel. He thought this might be due to a shifting wind, but
upon querying the boat's captain, he learned that the wind's direction had
remained constant. At that point, he realized that the vane's direction was
resulting from a coupling of the boat's motion with the wind direction.

At this point, Bradley made a profound connection: he likened the Earth
to the boat and the light from a star to the wind. He then realized that
the apparent position of the star was changing as the Earth moved in its
orbit. Bradley described this phenomenon in a letter to Halley, which was
read to the Royal Society in January 1729. In his letter, he named the phenomenon “aberration
of starlight,” because the stars appeared to be in a different position
that they actually were, due to the fact that they were being observed from
a moving body.

Bradley further realized that since his telescope was moving through space
along with the Earth, in order for the starlight to hit the eyepiece in the
center of his telescope, he would have to tilt the telescope in the Earth's
direction of motion, towards the apparent position of the star. He determined
that the angle at which the telescope must be tilted represents the ratio
of the speed at which the Earth is moving around the Sun divided by the speed
of light. Nowadays, thanks to Einstein's special theory of relativity, we
now know that a relativistic correction factor must be added to the speed
of light in the denominator of the stellar aberration ratio.

From his observations of Gamma Draconis, Bradley knew that the maximum angle
at which his telescope had to be tilted was tiny--approximately 20 arc-seconds.
Using this angle, and the velocity of the Earth moving around the Sun, known
in his day to be ~30 km/sec (~18.6 miles/sec), he calculated the speed of
light to be about 10,000 times faster than the orbital velocity of Earth
or ~300,000 km/sec (~186,000 miles/sec).

You can now see why the aberration of starlight plays a role in the GP-B
experiment. While constantly tracking the guide star, IM Pegasi, the telescope
on-board the spacecraft is always in motion--both orbiting the Earth once
every 97.5 minutes and along with the Earth, the spacecraft and telescope
are orbiting the Sun once a year. These motions result in two sources of
aberration of the starlight from IM Pegasi. The first is an orbital aberration,
which has a maximum angle of 5.1856 arcseconds, resulting from the spacecraft's
orbital speed of approximately 7 km/sec, relative to the speed of light.
(In the case of orbital aberration, the relativity correction is insignificant.).
The second is the now familiar annual aberration due to the Earth's orbital
velocity around the Sun, which when corrected for special relativity, amounts
to an angle of 20.4958 arcseconds.

In the GP-B experiment, the signals representing the drift in the gyroscope
spin axes over time are represented by voltages that have undergone a number
of conversions and amplifications by the time they are telemetered to Earth.
These conversions and amplifications impart a scale factor of unknown size
into the data, and early on in the development of the GP-B experimental concept
it was apparent that there needed to be a means of determining the size of
this gyro scale factor in order to see the true relativity signal. Initially,
it seemed that aberration of starlight was going to be a source of experimental
error bundled into the scale factor. But upon examining this issue more closely,
it suddenly became clear that, quite to the contrary, the orbital and annual
aberration of light from the guide star actually provided two built-in calibration
signals that would enable the gyro scale factor to be calculated with great
accuracy.

To see how this works, let's first take a closer look at how the orbital
aberration of the starlight from the guide star, IM Pegasi, is “seen” by
GP-B spacecraft. As mentioned earlier, the spacecraft orbits the Earth once
every 97.5 minutes. As the spacecraft emerges over the North Pole, the guide
star comes into the field of view of the science telescope, and the telescope
then locks onto the guide star. This begins what is called the “Guide
Star Valid (GSV)” phase of the orbit. At this point in its orbit, the
orientation of the spacecraft's velocity is directly towards the guide star,
and thus, there is no aberration of the star's light-it travels straight
down the center of the telescope. However, as the spacecraft moves down in
front of the Earth, the orientation of its velocity shifts in the orbital
direction until it becomes perpendicular to the direction of the light from
the guide star, slightly above the equator. This is the point of maximum
aberration since the telescope is now moving perpendicular to the guide star's
light. As the spacecraft moves on towards the South Pole, the aberration
recedes back to zero as the spacecraft moves under the Earth, directly away
from the guide star. At this point, the telescope unlocks from the guide
star, transitioning into what is called the “Guide Star Invalid (GSI)” phase
of the orbit. The navigational rate gyros on the outside of the spacecraft
maintain the telescope's orientation towards the guide star while the spacecraft
is behind the Earth, but we do not use the science gyro data during the GSI
phase.

During the GSV portion of each orbit, the telescope remains locked on the
guide star, with the spacecraft's micro thrusters adjusting the telescope's
pointing for the aberration of the guide star's light. This introduces a
very distinct, half-sine wave pattern into the telescope orientation. This
sinusoidal motion is also detected by the gyro pickup loops that are located
in the gyro housings, along the main axis of the spacecraft and telescope.
Thus, this very characteristic pattern, generated by the telescope and thrusters,
appears as a calibration signal in the SQUID Readout Electronics (SRE) data
for the gyros.

The annual aberration of the guide star's light works the same way as the
orbital aberration signal, but it takes an entire year to generate one complete
sine wave. Using the spacecraft's GPS system, we can determine the orbital
velocity of the spacecraft to an accuracy of better than one part in 100,000
(0.00001). Likewise, using Earth ephemeris data from the Jet Propulsion Lab
in Pasadena, CA, we can determine Earth's orbital velocity to equal or better
accuracy. We then use these velocities to calculate the orbital and annual
aberration values with extremely high precision, and in turn, we use these
very precise aberration values to calibrate the gyro pointing signals. It
is interesting to note that the amplitude of the sine wave generated by the
annual aberration is four times as large as the orbital aberration amplitude,
with peaks occurring is September and March. Because we launched GP-B in
April and started collecting science data in September, the effect of the
annual calibration signal did not become apparent in the data until this
past February-March, six to seven months into the science phase of the mission.
Thus, from March onward, both the annual and orbital aberration signals will
be used in the ongoing analysis of the science data.

UPDATED NASA/GP-B FACT SHEET AVAILABLE FOR DOWNLOADING

We recently updated our NASA Factsheet on the GP-B mission and experiment. You'll now find this 6-page document (Adobe Acrobat PDF format) listed as the last navigation link under "What is GP-B" in the upper left corner of this Web page. You can also click here to download a copy.

Drawings & Photos: The layered composite photo of
the GP-B spacecraft orbiting the Earth and the orbital aberration diagrams
were created by GP-B Public Affairs Coordinator, Bob Kahn using Adobe Photoshop
and Adobe Illustrator. Mr. Kahn also took the photos of the Greenwich Observatory
and Museum and the photo of the GP-B MOC during gyro spinup. The photos of
the gyroscope housing and the UV lamp discharge system are from the GP-B Image
Archive here at Stanford. The photo of the McMurdo ground station is courtesy
of NASA. The portrain of James Bradley was painted by Thomas Hudson. Click
on the thumbnails to view these images at full size.